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Nuclear weighted composition operators on weighted Banach spaces of analytic functions


Authors: José Bonet, M. Carmen Gómez-Collado, Enrique Jordá and David Jornet
Journal: Proc. Amer. Math. Soc. 149 (2021), 311-321
MSC (2010): Primary 47B10, 47B33
DOI: https://doi.org/10.1090/proc/15223
Published electronically: September 18, 2020
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Abstract: We characterize nuclear weighted composition operators $ W_{\psi ,\varphi }f=\psi (f\circ \varphi )$ on weighted Banach spaces of analytic functions with sup-norms. Consequences about nuclear composition operators on Bloch type spaces are presented. They extend previous work by Fares and Lefèvre on nuclear composition operators on Bloch spaces. Examples of nuclear as well as compact and non-nuclear weighted composition operators are given.


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Additional Information

José Bonet
Affiliation: Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, E-46071 Valencia, Spain
ORCID: 0000-0002-9096-6380
Email: jbonet@mat.upv.es

M. Carmen Gómez-Collado
Affiliation: Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, E-46071 Valencia, Spain
ORCID: 0000-0003-0604-1009
Email: mcgomez@mat.upv.es

Enrique Jordá
Affiliation: EPS Alcoy, Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Plaza Ferrándiz y Carbonell s/n, E-03801 Alcoy, Spain
ORCID: 0000-0003-2980-1699
Email: ejorda@mat.upv.es

David Jornet
Affiliation: Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, E-46071 Valencia, Spain
MR Author ID: 693618
ORCID: 0000-0002-3531-6203
Email: djornet@mat.upv.es

DOI: https://doi.org/10.1090/proc/15223
Received by editor(s): April 21, 2020
Received by editor(s) in revised form: June 4, 2020
Published electronically: September 18, 2020
Additional Notes: The research of the authors was partially supported by the project MTM2016-76647-P. The research of the first author was partially supported by the project GV Prometeo 2017/102.
Communicated by: Javad Mashreghi
Article copyright: © Copyright 2020 American Mathematical Society